Campo Santo Teutonico

I was told that the "Campo Santo Teutonico"
(Teutonic College and Graveyard) within Vatican City
(number 60 on
this map) is actually technically not part
of Vatican City, but the last little bit of the Holy Roman Empire.
Supposedly it is administered jointly by the
ambassadors of Austria, Germany, Belgium, and Netherlands.
(The only confirmation of this I've found on the web is
in German, and says that this was part of the 1929 Lateran Treaty
that established Vatican City.
Also: the border on
this map shows it not being part of VC.)